Is there a way to make dynamic paint affect the reaction diffusion from tissue?
Here is a way to visualize reaction diffusion, it takes a few steps but it seems to work I guess. Unfortunately, it does not seem that dynamic paint will directly work to control reaction diffusion, but we can use other ways to visualize it.
Starting with a densely subdivided quad-sphere, I have set up reaction diffusion and painted some random pattern on vertex group B with animation running. One thing I am also doing here is adding a few keyframes in the scale parameter throughout the timeline to add a bit of variation in the animation.
Here are my settings:


Bake the reaction diffusion before moving on.


In object mode, make a copy of the object, and do not move it. 
Shift + D then Enter.
The copy and original must be in the same place for the next step to work properly.

In Weight Paint again, first select the original object, then select the copy and go to Weights&gt;transfer weights to copy the weights from the original to copy. This will copy the reaction diffusion from the original mesh to the copy, also allowing the animated weights to be used in modifiers in object mode.
Now you will be able to use the vertex groups with any combination of modifiers, such as displace, mask, etc.
For example, here is the quadsphere with just a displace modifier using the B vertex group.

Here is the .blend if you would like to inspect it